The single-crystal growth of extended solids is an active area of solid-state chemistry driven by the discovery of new physical phenomena. Although many solid-state compounds have been discovered over the last several decades, single-crystal growth of these materials in particular enables the determination of physical properties with respect to crystallographic orientation and the determination of properties without possible secondary inclusions. The synthesis and discovery of new classes of materials is necessary to drive the science forward, in particular materials properties such as superconductivity, magnetism, thermoelectrics, and magnetocalorics. Our research is focused on structural characterization and determination of physical properties of intermetallics, culminating in an understanding of the structure-property relationships of single-crystalline phases. We have prepared and studied compounds with layered motifs, three-dimensional magnetic compounds exhibiting anisotropic magnetic and transport behavior, and complex crystal structures leading to intrinsically low lattice thermal conductivity. In this Account, we present the structural characteristics and properties that are important for understanding the magnetic properties of rare earth transition metal intermetallics grown with group 13 and 14 metals. We present phases adopting the HoCoGa5 structure type and the homologous series. We also discuss the insertion of transition metals into the cuboctahedra of the AuCu3 structure type, leading to the synthetic strategy of selecting binaries to relate to ternary intermetallics adopting the Y4PdGa12 structure type. We provide examples of compounds adopting the ThMn12, NaZn13, SmZn11, CeCr2Al20, Ho6Mo4Al43, CeRu2Al10, and CeRu4Al16-x structure types grown with main-group-rich self-flux methods. We also discuss the phase stability of three related crystal structures containing atoms in similar chemical environments: ThMn12, CaCr2Al10, and YbFe2Al10. In addition to dimensionality and chemical environment, complexity is also important in materials design. From relatively common and well-studied intermetallic structure types, we present our motivation to work with complex stannides adopting the Dy117Co57Sn112 structure type for thermoelectric applications and describe a strategy for the design of new magnetic intermetallics with low lattice thermal conductivity. Our quest to grow single crystals of rare-earth-rich complex stannides possessing low lattice thermal conductivity led us to discover the new structure type Ln30Ru4+xSn31-y (Ln = Gd, Dy), thus allowing the correlation of primitive volumes with lattice thermal conductivities. We highlight the observation that Ln30Ru4+xSn31-y gives rise to highly anisotropic magnetic and transport behavior, which is unexpected, illustrating the need to measure properties on single crystals.